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Home Scientific Thematic Programmes Algebraic Geometry, Cohomology and Representation Theory 2005-2006 PIMS Home About PIMS Contact Us PIMS Offices ... PIMS only Algebraic Geometry, Cohomology and Representation Theory 2005-2006 Overview For the most part, these advances have been brought about by the fact that algebraic geometry poses intrinsically interesting and relevant problems, and has the property of developing the mathematical tools to solve them. It has therefore attracted many talented mathematicians, many of whom are not formally trained in the area, but have realized its value. This has further stimulated new connections between algebraic geometry and other disciplines: e.g. combinatorics, cryptography, statistics, and quantum computing. Algebraic geometry has also given us new insight into the nature of algebraic groups and Galois cohomology. During the last two decades many exciting fundamental theorems have been established due to the introduction of new powerful techniques from algebraic topology and algebraic geometry. For instance, Voevodsky's use of homotopy and cobordism theory have resulted first in the solution of Milnor conjecture and, more recently, the Bloch-Kato conjecture. Further development of these ideas is crucial. The PIMS CRG has many people working in the cutting edge in several of the above areas. Among the specialties represented by our varied group are algebraic stacks, geometric invariant theory, algebraic group actions, toric varieties and torus actions, algebraic cycles, Gromov-Witten theory, arithmetic algebraic geometry, classification theory, algebraic representation theory, Lie theory and Schubert varieties, group cohomology.

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